An update on spaces of embeddings

  • Date: 03/05/2008

Ryan Budney (University of Victoria)


University of British Columbia


The Cerf-Morlet comparison theorem states that the group of
diffeomorphisms of the compact n-ball which is the identity on the
boundary is an (n+1)-fold loop space, whose (n+1)-fold de-looping is
the homotopy-quotient of the group of the PL-homeomorphisms of R^n by
the smooth homeomorphisms of R^n. In 2002 I observed that this
Cerf-Morlet iterated loop space structure generalizes to an iterated
loop space structure on the space of embeddings of R^j in R^n which are
standard outside of a fixed ball and equipped with a trivialization of
a tubular neighbourhood. This talk will be about the homotopy-type of
these embedding spaces, viewed as iterated loop-spaces. I've been able
to make the most progress in the case (j,n)=(1,3), which I will
describe in detail. My most recent work on this has to do with a
`realization problem' associated to the (j,n)=(1,3) case which boils
down to a study of the symmetry groups of a certain family of
hyperbolic links in S3 together with a family of natural
representations of these symmetry groups.

Other Information: 

Algebra/Topology Seminar 2008